I recently came across a book just published by Jason Ross, entitled The Battle for Light: Fermat vs. Descartes: A Sourcebook on Pierre de Fermat’s Principle of Least Time. Therein, Ross presents, in English, the correspondence Pierre de Fermat (1607-1665) undertook with René Descartes (1596-1650) and the latter’s followers. The correspondence was taken from the collected works of Fermat
Seeing the history of these scientific debates is very cool. Thank you for this!
The principle of least action is one of the many consequences that can be deduced from taking the conservation of energy seriously. That it has been discovered and rediscovered by so many different paths is beautifully ironic.
I’m interested in your mention of Huygens' quote, where he appears to side with Fermat's principle of least time over Des Cartes view. Huygens emphasizes that light chooses the path of least time, not necessarily least distance. However, if Huygens understood that least time implies light travels at varying speeds in different media, why would he then disagree with Descartes' assertion that light slows down in denser materials? It seems like a contradiction. Could you please clarify Huygens' position on this apparent discrepancy?
The "principle of least time" does not truly explain refraction or reflection. It is better understood as a *feature* of refraction and reflection.
Consider reflection. It's not because of "principle of least time" that the photon hits the reflective surface and exits at the same angle. It's a resultant feature of the reflection event.
If one actually strictly believes "principle of least time" is the cause, then the photon should just travel straight from A to B and "by principle" avoid the mirror.
Using 20th century concepts such as the photon to discuss the merits of a 17th century scientist, namely Fermat, is, with all due respect, pretty dubious.
The principle of least time states clearly that of all the possible paths interacting with the mirror, the one taken by light takes the least time. So your writing "then the photon should just travel straight from A to B and "by principle" avoid the mirror" simply means that you do not understand the concept.
What is your concept of a unit of light that isn't a photon?
> "The principle of least time states clearly that of all the possible paths interacting with the mirror"
There is a wrong assumption in there, the assumption that there are many possible paths for a laser beam, and that because of a "principle of least time" the laser beam takes a certain path.
If you had a laser pointer and pointed it at a mirror next to you, it's not because of a "principle of least time" that the laser beam goes wherever it goes. The laser beam goes where it does because of the initial vector of emission, and then it travels step by step.
"Principle of least time" is not a cause. And it's not a principle. That's what I'm calling out. It's a resultant feature of the path, once you know the start A and end B (which may not necessarily be known in advance).
Seeing the history of these scientific debates is very cool. Thank you for this!
The principle of least action is one of the many consequences that can be deduced from taking the conservation of energy seriously. That it has been discovered and rediscovered by so many different paths is beautifully ironic.
Nice
I was hoping for the proof that AB-BC is shorter time.
Hmmm, maybe a follow-up post would be appropriate.
I’m interested in your mention of Huygens' quote, where he appears to side with Fermat's principle of least time over Des Cartes view. Huygens emphasizes that light chooses the path of least time, not necessarily least distance. However, if Huygens understood that least time implies light travels at varying speeds in different media, why would he then disagree with Descartes' assertion that light slows down in denser materials? It seems like a contradiction. Could you please clarify Huygens' position on this apparent discrepancy?
Descartes thought that light goes faster in denser materials, not slower. Fermat thought the opposite. Maybe this is worthy of a follow-up post.
Ahh. That makes sense now. Just like sound travels faster in denser media. I’d be very interested in the details.👍🏼
The "principle of least time" does not truly explain refraction or reflection. It is better understood as a *feature* of refraction and reflection.
Consider reflection. It's not because of "principle of least time" that the photon hits the reflective surface and exits at the same angle. It's a resultant feature of the reflection event.
If one actually strictly believes "principle of least time" is the cause, then the photon should just travel straight from A to B and "by principle" avoid the mirror.
Using 20th century concepts such as the photon to discuss the merits of a 17th century scientist, namely Fermat, is, with all due respect, pretty dubious.
The principle of least time states clearly that of all the possible paths interacting with the mirror, the one taken by light takes the least time. So your writing "then the photon should just travel straight from A to B and "by principle" avoid the mirror" simply means that you do not understand the concept.
What is your concept of a unit of light that isn't a photon?
> "The principle of least time states clearly that of all the possible paths interacting with the mirror"
There is a wrong assumption in there, the assumption that there are many possible paths for a laser beam, and that because of a "principle of least time" the laser beam takes a certain path.
If you had a laser pointer and pointed it at a mirror next to you, it's not because of a "principle of least time" that the laser beam goes wherever it goes. The laser beam goes where it does because of the initial vector of emission, and then it travels step by step.
"Principle of least time" is not a cause. And it's not a principle. That's what I'm calling out. It's a resultant feature of the path, once you know the start A and end B (which may not necessarily be known in advance).